Question: Which of the following numbers is a multiple of 6? ${49,59,100,107,108}$
The multiples of $6$ are $6$ $12$ $18$ $24$ ..... In general, any number that leaves no remainder when divided by $6$ is considered a multiple of $6$ We can start by dividing each of our answer choices by $6$ $49 \div 6 = 8\text{ R }1$ $59 \div 6 = 9\text{ R }5$ $100 \div 6 = 16\text{ R }4$ $107 \div 6 = 17\text{ R }5$ $108 \div 6 = 18$ The only answer choice that leaves no remainder after the division is $108$ $ 18$ $6$ $108$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $6$ are contained within the prime factors of $108$ $108 = 2\times2\times3\times3\times3 6 = 2\times3$ Therefore the only multiple of $6$ out of our choices is $108$. We can say that $108$ is divisible by $6$.